Geometry is by its very nature, graphic.Not so much as to effect an “X” rating, but one that nonetheless carries its own messages.More than most disciplines, geometry is about the symbolism of form and what that conveys to the observer.

Bruce Rawles <http://www.intent.com/sg/> introduces his view of Sacred Geometry by noting that, “In nature, we find patterns, designs and structures from the most minuscule particles, to expressions of life discernible by human eyes, to the greater cosmos. These inevitably follow geometrical archetypes, which reveal to us the nature of each form and its vibrational resonances. They are also symbolic of the underlying metaphysical principle of the inseparable relationship of the part to the whole. It is this principle of oneness underlying all geometry that permeates the architecture of all form in its myriad diversity. This principle of interconnectedness, inseparability and union provides us with a continuous reminder of our relationship to the whole, a blueprint for the mind to the sacred foundation of all things created.”[emphasis added]

This brief paragraph says in a nutshell why much of geometry is called Sacred Geometry, why much of mathematics is called Sacred Mathematics, and why numbers are inherently basic to Philosophy (aka F-lo-Sophia).From the most profound symbolism of a Vesica Pisces to the fundamentals of Transcendental Numbers and Nines, the point can be made over and over again that any chosen divinity is of necessity going to be a supreme being who can work the numbers!

Graphically, there is the distinction between two-dimensional (“plane geometry”) and three-dimensional (“solid geometry”).It is possible, for example, to begin with a Vesica Pisces and construct regular polygons of three thru nine sides.Euclid’s The Elements begins with a mere five postulates, and creates all of plane geometry.The Harmony of the Spheres, with its three-dimensional implication, can be approximated as a plane (i.e. the plane of the Zodiac), and thus the geometries shown in A Book of Coincidence provide a graphic two-dimensional description of the planetary orbits.Meanwhile, the Platonic Solids, and other solids (http://mathworld.wolfram.com/JohnsonSolid.html)provide the impetus for creating elaborate and potentially profound shapes such as two interlocked tetrahedra -- the latter which is important in Hyperdimensional Physics and the “hot spots” on the planets at latitudes of 19.47 degrees (north or south).

Meanwhile, the strict adherence to Sacred Geometry by ancient and other architects

is evident in: The Parthenon of Athens Greece

(which is based on the harmonic relationship of

5/4), the Sri Yantra of 9 interlocking triangles,

the plan of the Osirian second temple, the

United Nations building in New York City, and

the Ka-ba (cube) at Mecca.

Then there is also Leonardo da Vinci’s famous drawing of an ideal man with all of the dimensions of sacred geometry and the five pointed star incorporated in the drawing.

The five pointed star is, in fact, pervasive in the modern world, from stars on a flag, to oil company symbols, to the basis of modern Wicca, to the connecting links between planets (see A Book of Coincidence).The connection to the Golden Mean undoubtedly yields an emotional, physical, and/or spiritual reaction when we encounter these symbols, such that their use by man is clearly predicated on a knowledge of these basic principles.In other words, never discount the ability of marketing to use any effective means at its disposal to make a buck.(But only God can make a deer.)

In the case of the five-pointed star (geometry-wise), if the side of a pentagon is 1, then:

AB = 1

EG = FB = 1

EB = F (1.618...)

GB = f (0.618...) = 1/F

GI = FG = 1 - f = f2 (0.328...)

JG = f3 (0.236...)

Then there is the truly weird, one of the Crop Circles which appeared in England in the 1990s on the estate of Andrew Lloyd Webber (much to the chagrin on his security personnel) in which the five pointed star was transfigured into what might be likened as to a dancing clown -- but which still maintained the pentagonal angles, and the Golden Mean relative distances.

Another intriguing graphic is the means by which the 5/4th trick of “squaring the circle” or use of Fibonacci Numbers, can be utilized to divide a circle into -- of all things! -- seven equal parts.Or roughly equal as the resulting angles are 51.317812... degrees (i.e. arc-cosine of 5/8), as opposed to 360/7 = 51.42857142...The trick is to lay out equal distances on a string and form triangles with sides of 8, 8, and 10.Then use the cosine of the near side (5) of the interior angle divided by the hypotenuse (8), to calculate the angle.

While there is a minor error of 0.22%, for the ancient (and modern) builders, this is not a problem at all.As a quick and dirty method, it is unsurpassed -- even when it is also possible to create a seven sided polygon from the Vesica Pisces.

By the way, an excellent book, with over two hundred illustrations (roughly one-fourth in color) is Robert Lawlor’s Sacred Geometry, Philosophy and Practice, Thames and Hudson, London, 1982.

In the realm of three-dimensional geometries, the Platonic Solids are the most notable, along with pyramids of various shapes and sizes -- including The Great Pyramids of both Giza (Egypt) and Teotihuacan (Mexico).But that’s another story.(Or link.)